Permutation & Combination Calculator
Calculate nPr and nCr (combinations) exactly for large n using BigInt, plus factorials, with the formulas and substituted values shown.
Runs on your device
Result
Results appear here as you type.
What it does
How many ways can 5 people sit in 3 chairs (permutations, order matters) or how many 3-person teams can be chosen from 5 (combinations, order does not)? Results are exact, even for n up to 1,000.
How to use it
- Enter n (total items) and r (items chosen).
- Read nPr and nCr.
- Follow the formula lines.
Example
5P3 = 60, 5C3 = 10. Select Try an example above to see it.
When it helps
- Probability homework.
- Counting test cases.
- Lottery and password space estimates.
Questions
When do I use permutations?
When order matters (arrangements, rankings, PIN codes). Use combinations when it does not (teams, hands of cards).
What is 0!?
1, by definition, which makes nC0 = 1.
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